The spheroidal wave functions are found to have extensive applications in many branches of physics and mathematics. We use the perturbation method in supersymmetric quantum mechanics to obtain the analytic ground eige...The spheroidal wave functions are found to have extensive applications in many branches of physics and mathematics. We use the perturbation method in supersymmetric quantum mechanics to obtain the analytic ground eigenvalue and the ground eigenfunction of the angular spheroidal wave equation at low frequency in a series form. Using this approach, the numerical determinations of the ground eigenvalue and the ground eigenfunction for small complex frequencies are also obtained.展开更多
To enhance the potential application of thermally activated delayed fluorescence(TADF)molecular materials,new functions are gradually cooperated to the TADF molecules.Aggregation induced emission can effectively solve...To enhance the potential application of thermally activated delayed fluorescence(TADF)molecular materials,new functions are gradually cooperated to the TADF molecules.Aggregation induced emission can effectively solve the fluorescence quenching problem for TADF molecules in solid phase,thus aggregation-induced delayed fluorescence(AIDF)molecules were recently focused.Nevertheless,their luminescent mechanisms are not clear enough.In this work,excited state properties of an AIDF molecule DMF-BP-DMAC[reported in Chemistry-An Asian Journal 14828(2019)]are theoretically studied in tetrahydrofuran(THF)and solid phase.For consideration of surrounding environment,the polarizable continuum method(PCM)and the combined quantum mechanics and molecular mechanics(QM/MM)method were applied for solvent and solid phase,respectively.Due to the increase of the transition dipole moment and decrease of the energy difference between the first single excited state(S1)and the ground state(S0),the radiative rate is increased by about 2 orders of magnitude in solid phase.The energy dissipation of the non-radiative process from S1 to S0 is mainly contributed by low-frequency vibrational modes in solvent,and they can be effectively suppressed in aggregation,which may lead to a slow non-radiation process in solid phase.Both factors would induce enhanced luminescence efficiency of DMF-BP-DMAC in solid phase.Meanwhile,the small energy gap between S1 and triplet excited states results in high reverse intersystem crossing(RISC)rates in both solvent and solid phase.Therefore,TADF is confirmed in both phases.Aggregation significantly influences both the ISC and RISC processes and more RISC channels are involved in solid state.The enhanced delayed fluorescence should be induced by both the enhanced fluorescent efficiency and ISC efficiency.Our calculation provides a reasonable explanation for experimental measurements and helps one to better understand the luminescence mechanism of AIDF molecules.展开更多
Spin-weighted spheroidal wave functions play an important role in the study of the linear stability of rotating Kerr black holes and are studied by the perturbation method in supersymmetric quantum mechanics. Their an...Spin-weighted spheroidal wave functions play an important role in the study of the linear stability of rotating Kerr black holes and are studied by the perturbation method in supersymmetric quantum mechanics. Their analytic ground eigenvalues and eigenfunctions are obtained by means of a series in low frequency. The ground eigenvalue and eigenfunction for small complex frequencies are numerically determined.展开更多
基金Project supported by the National Natural Science Foundation of China(Grant Nos.10875018 and 10773002)
文摘The spheroidal wave functions are found to have extensive applications in many branches of physics and mathematics. We use the perturbation method in supersymmetric quantum mechanics to obtain the analytic ground eigenvalue and the ground eigenfunction of the angular spheroidal wave equation at low frequency in a series form. Using this approach, the numerical determinations of the ground eigenvalue and the ground eigenfunction for small complex frequencies are also obtained.
基金the National Natural Science Foundation of China(Grant Nos.11874242,11974216,and 11904210)Shandong Provincial Natural Science Foundation,China(Grant No.ZR2019MA056)Taishan Scholar Project of Shandong Province,China,and the China Postdoctoral Science Foundation(Grant No.2018M642689).
文摘To enhance the potential application of thermally activated delayed fluorescence(TADF)molecular materials,new functions are gradually cooperated to the TADF molecules.Aggregation induced emission can effectively solve the fluorescence quenching problem for TADF molecules in solid phase,thus aggregation-induced delayed fluorescence(AIDF)molecules were recently focused.Nevertheless,their luminescent mechanisms are not clear enough.In this work,excited state properties of an AIDF molecule DMF-BP-DMAC[reported in Chemistry-An Asian Journal 14828(2019)]are theoretically studied in tetrahydrofuran(THF)and solid phase.For consideration of surrounding environment,the polarizable continuum method(PCM)and the combined quantum mechanics and molecular mechanics(QM/MM)method were applied for solvent and solid phase,respectively.Due to the increase of the transition dipole moment and decrease of the energy difference between the first single excited state(S1)and the ground state(S0),the radiative rate is increased by about 2 orders of magnitude in solid phase.The energy dissipation of the non-radiative process from S1 to S0 is mainly contributed by low-frequency vibrational modes in solvent,and they can be effectively suppressed in aggregation,which may lead to a slow non-radiation process in solid phase.Both factors would induce enhanced luminescence efficiency of DMF-BP-DMAC in solid phase.Meanwhile,the small energy gap between S1 and triplet excited states results in high reverse intersystem crossing(RISC)rates in both solvent and solid phase.Therefore,TADF is confirmed in both phases.Aggregation significantly influences both the ISC and RISC processes and more RISC channels are involved in solid state.The enhanced delayed fluorescence should be induced by both the enhanced fluorescent efficiency and ISC efficiency.Our calculation provides a reasonable explanation for experimental measurements and helps one to better understand the luminescence mechanism of AIDF molecules.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 10875018 and 10773002)
文摘Spin-weighted spheroidal wave functions play an important role in the study of the linear stability of rotating Kerr black holes and are studied by the perturbation method in supersymmetric quantum mechanics. Their analytic ground eigenvalues and eigenfunctions are obtained by means of a series in low frequency. The ground eigenvalue and eigenfunction for small complex frequencies are numerically determined.
